Grid Turbulence in Dilute High-Polymer Solutions 

 1 1 1 — I I I I I I 1 1 — I — I I I M I I I r 



I I I I I 



I I I I I I I I 



Fig. 23 - Inertial spectral transfer time, calculated (12) 

 from a Heisenberg spectrum. The points are from grid- 

 turbulence measurements by Uberoi (13). 



we may expect experimentally significant viscoelastic effects upon the grid tur- 

 bulence to first appear at k/k^ ~ 1/2, and we presume the effect would become 

 significant when 



t re/z.)i/V2 



(8) 



The molecular theories (14-16) which predict the value of t^ are for sufficiently 

 dilute solutions that the macromolecular coils are well separated. Thus 



100 Voh^l^ 

 Na^bT 



(9) 



,0 is the solvent viscosity; [t^] is the intrinsic viscosity for vanishing 

 steady shear rate or vanishing frequency of infinitesimal oscillatory shear; in is 

 the molecular weight; N^^ is the Avogadro constant; kg is the Boltzman constant; 

 and T is the absolute temperature. The numerical constant a varies somewhat 

 with the theory, but can be taken as 1/2 for this work. The factor of 100 ap- 

 pears when [t]] is given in the usual units of dl/g. 



Comparison of the molecular theory predictions with experimental meas- 

 urements have only been made for solutions which are not "dilute" in the sense 

 c' [t]] « 1. Reasonable agreement for well-characterized solutions, i.e., of 

 narrow or known molecular weight distributions, has been obtained by many 



67 



